Translation snapping toggle - Specific dynamic snapping
It's not so much that you can't change targets while snapping, its more that generally if you are snapping that usually means you are using some sort of  transform operator already.

Now transform operators are generally Modal operators, so that means while they run there is generally a predefined set of actions you can preform, limited by what Blender developers coded into that operator.

As far as I know you could not invoke wm.context_toggle while an operator is already running.

That being said some of the operators do provide some snapping options you can configure. Just go to File > User Preferences > Input search for a transform operator like Translate if you expand it you can control its specific sub-keymap, which includes some basic snapping options like Invert or toggling on and off.